A case study on the choice, interpretation and checking of multilevel models for longitudinal binary outcomes.

Area of Science:

• Statistical modeling
• Longitudinal data analysis
• Biostatistics

Background:

• Multilevel (hierarchical/random effects) models are increasingly used for longitudinal binary data.
• These models often use a logistic-normal specification, analogous to models for continuous data.
• Interpretation and diagnostics for these models, especially compared to Generalized Estimating Equations (GEE), remain challenging.

Purpose of the Study:

• To investigate the interpretability of coefficients and inferences from random-effects models for binary outcomes.
• To identify appropriate diagnostic checks for assessing the fit of these multilevel models.
• To evaluate a discrete-mixture alternative to the standard logistic-normal model using Bayesian methods.

Main Methods:

• An extended case study using adolescent smoking data from a large cohort study.
• Bayesian estimation to fit a discrete-mixture model as an alternative to the standard logistic-normal multilevel model.
• Posterior predictive checking to assess model fit for both multilevel approaches.

Main Results:

• Parameter estimates from the logistic-normal and discrete-mixture models showed surprising parallels.
• These parallels raise questions about the interpretability of 'subject-specific' regression coefficients in standard multilevel models.
• Posterior predictive checks indicated a significant lack of fit for both multilevel models examined.

Conclusions:

• The interpretability of standard multilevel models for binary outcomes requires careful consideration.
• Current multilevel models may not adequately fit longitudinal binary data, necessitating improved diagnostic tools.
• Lessons from this case study offer guidance for future research on multilevel modeling of binary longitudinal data.